Question

What is the surface area of the regular pyramid below?A. 648 sq. unitsB. 552 sq. unitsC. 396 sq. unitsD. 522 sq. units

Answer 1

Step 1:

Concept: Calculate the area of each face and add all together to get the surface area of the pyramid.

The regular pyramid below have 4 triangles and a square

Step 2: Apply the area formula to find the area of the 4 triangles and a square.

`\begin{gathered} \text{Area of a triangle = }\frac{Base\text{ x Height}}{2} \\ \text{Area of the square base = Length x Length} \end{gathered}`

Step 3:

Given data for the triangle

Height = 21

Base = 12

`\begin{gathered} Area\text{ of a triangle = }\frac{Base\text{ x Height}}{2} \\ =\text{ }\frac{21\text{ x 12}}{2} \\ =\text{ }(252)/(2) \\ =126\text{ sq. units} \\ \text{Area of the four triangles = 4 x 126 = 504 sq. units} \end{gathered}`

Step 4: Find the area of the square

Given data for the square

Length = 12

Area = length x length = 12 x 12 = 144 sq. units

Step 5: Add the area of the four triangles and the square.

Surface area of the regular pyramid = 504 + 144

= 648 sq. units